Parameterizing the periodic orbit by the abscissa \(\xi \)  of
intersection point between oval \(\Gamma \)  with positive half
\(x-\) axis, denoted by \(\Gamma _{\xi }\) . Concerning the bifurcation of critical periods from the linear isochronous center, Variation Lemma 3.2 of [1]} stated as follows proposes a necessary condition to the persistence of \(2\pi -\) periodic solutions.
